Stock index prediction and uncertainty analysis using multi-scale nonlinear ensemble paradigm of optimal feature extraction, two-stage deep learning and Gaussian process regression

Reliable prediction of stock indexes can be highly valuable for financial decision-making and risk management. The stock market is a highly complicated nonlinear system which makes it difficult to present accurate predictors. In this paper, an innovative multi-scale nonlinear ensemble paradigm is proposed for stock index prediction and uncertainty analysis, which consists of an optimal feature extraction including variational mode decomposition and auto-encoder, a two-stage deep learning based on recurrent neural network and long short-term memory, and Gaussian process regression. The optimal feature extraction is proposed to extract the optimal features of stock index fluctuations and eliminate the disturbance of illusive components. The two-stage deep learning is developed to conduct the prediction of each feature sub-signal and implement its nonlinear integration. The Gaussian process regression is utilized to construct the interval prediction of the original stock signal and analyze the uncertainties of stock market. The validity of the developed model is verified by the data from S&P 500, Dow Jones index and NASDAQ. After a series of comparisons, the mean absolute percentage errors of the proposed model in S&P 500, Dow Jones index and NASDAQ are 0.55%, 0.65% and 1.11%, respectively. These results fully verify the effectiveness of proposed model. (C) 2021 Elsevier B.V. All rights reserved.